Problem: Simplify the following expression and state the condition under which the simplification is valid. $r = \dfrac{t^2 - 25}{t + 5}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = t$ $ b = \sqrt{25} = 5$ So we can rewrite the expression as: $r = \dfrac{({t} + {5})({t} {-5})} {t + 5} $ We can divide the numerator and denominator by $(t + 5)$ on condition that $t \neq -5$ Therefore $r = t - 5; t \neq -5$